Question

You have a modem that can operate at a symbol rate of 9,600 . Design a modulation system to allow the modem to transmit at a data rate of 76,800 bps. Specifically, you need to indicate how many amplitude levels and phase levels this modem must be able to generate. (Your design should vary both the amplitude and the phase of the carrier wave signal.)

a) Required total alternative signal states:
b) Amplitude levels:
c) Phase levels

Answer 1

The modem would need to generate a total of 8 alternative signal states, which could be accomplished with 3 amplitude levels and 3 phase levels. This design would use Quadrature Amplitude Modulation (QAM).

Step-by-step explanation:

To design a modulation system for a modem that operates at a symbol rate of 9,600 to transmit data at 76,800 bps, while variating both amplitude and phase, we would use Quadrature Amplitude Modulation (QAM). The total number of alternative signal states (S) needed can be calculated by the formula S = Data rate / Symbol rate. In this case, S = 76,800 bps / 9,600 symbols per second = 8. Therefore, to achieve this, we need to determine the number of amplitude levels (A) and phase levels (P) such that A x P = S.

Since we have 8 signal states and we want to vary both amplitude and phase, a simple solution would be to use 4 amplitude levels and 2 phase levels (4 amplitude levels x 2 phase levels = 8 signal states). However, to optimize the signal quality and reliability, a common practice would be to have an equal number of phases and amplitudes levels when possible, which suggests 8 signal states can be achieved with 3 levels of amplitude and 3 levels of phase (3x3=9), but only 8 of the 9 combinations would be used.

So the modem must be able to generate:

• Required total alternative signal states: 8
• Amplitude levels: 3 (assuming we use only 8 out of the 9 possible combinations)
• Phase levels: 3 (assuming we use only 8 out of the 9 possible combinations)